Topological Quantum Computation

We give a rigorous development of the construction of new braided fusion categories from a given category known as zesting. This method has been used in the past to provide categorifications of new fusion rule algebras, modular data, and minimal …

Acyclic anyon models are non-abelian anyon models for which thermal anyon errors can be corrected. In this note, we characterize acyclic anyon models and raise the question whether the restriction to acyclic anyon models is a deficiency of the …

We study spin and super-modular categories systematically as inspired by fermionic topological phases of matter, which are always fermion parity enriched and modelled by spin topological quantum field theories at low energy. We formulate a 16-fold …

Given a fusion category $\mathcal{C}$ and an indecomposable $\mathcal{C}$-module category $\mathcal{M}$, the fusion category $\mathcal{C}_{\mathcal{M}}^{*}$ of $\mathcal{C}$-module endofunctors of $\mathcal{M}$ is called the (Morita) dual fusion …

Topological order of a topological phase of matter in two spacial dimensions is encoded by a unitary modular (tensor) category (UMC). A group symmetry of the topological phase induces a group symmetry of its corresponding UMC. Gauging is a well-known …

We address the problem of determining the obstruction to existence of solutions of the hexagon equation for abelian fusion rules and the classification of prime abelian anyons.

We prove that every braiding over a unitary fusion category is unitary and every unitary braided fusion category admits a unique unitary ribbon structure.

We investigate braid group representations associated with unitary braided vector spaces, focusing on a conjecture that such representations should have virtually abelian images in general and finite image provided the braiding has finite order. We …

We classify Galois objects for the dual of a group algebra of a finite group over an arbitrary field.

We study exact module categories over the representation categories of finite-dimensional quasi-Hopf algebras. As a consequence, we classify exact module categories over some families of pointed tensor categories with cyclic group of invertible …